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Constraint Preserving Schemes Using Potential-Based Fluxes I. Multidimensional Transport Equations

Published online by Cambridge University Press:  20 August 2015

Siddhartha Mishra and
Eitan Tadmor
Siddhartha Mishra*
Affiliation:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway
Eitan Tadmor*
Affiliation:
Center of Scientific Computation and Mathematical Modeling (CSCAMM), and Department of Mathematics, and Institute for Physical Sciences and Technology (IPST), University of Maryland, MD 20742-4015, USA
*
Email:siddharm@cma.uio.no
Corresponding author.Email:tadmor@cscamm.umd.edu
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Abstract

We consider constraint preserving multidimensional evolution equations. A prototypical example is provided by the magnetic induction equation of plasma physics. The constraint of interest is the divergence of the magnetic field. We design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the constraint. The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered potentials. The potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving equations. We present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution, while being constraint preserving.

Keywords

65M0635L65Multidimensional evolution equationsmagnetohydrodynamicsfinite-differencefinite volume schemesconstraint transportpotential-based schemes

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Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011, pp. 688 - 710
Copyright
Copyright © Global Science Press Limited 2011

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